A take-away message is that, among the learning rate selection methods considered here, the GPC algorithm of [1]} seems to be best suited overall for calibrating the generalized Bayes credible regions. This is not surprising, given that is precisely what the GPC algorithm is designed to do. GPC is computationally more expensive than, say, the method of [2]}, but our results here suggest that the extra time/effort is well spent. Although GPC has been shown to have very good empirical performance here and in a number of other references, there is still no formal proof that it does indeed provide valid posterior uncertainty quantification.
